The system of equations provided in the image is:

1. $y = x + 5$
2. $y = 10x - 6$

To solve this system, let's set the two expressions for $y$ equal to each other since both equal $y$:

$x + 5 = 10x - 6$

Now, let's solve for $x$:

$x + 5 = 10x - 6$

Subtract $x$ from both sides:

$5 = 9x - 6$

Next, add 6 to both sides:

$11 = 9x$

Finally, divide both sides by 9:

$x = \frac{11}{9} \approx 1.22$

Now, substitute $x = 1.22$ into either of the original equations to find $y$. Let's use $y = x + 5$:

$y = 1.22 + 5 = 6.22$

So, the solution to the system of equations is:

$(x, y) \approx (1.22, 6.22)$

Would you like further clarification or details on the steps?

Here are some related questions to explore further:

1. How do you solve a system of equations graphically?
2. What happens if the two lines in the system are parallel?
3. How can you solve a system of equations using substitution or elimination methods?
4. What is the meaning of the solution to a system of equations in real-world contexts?
5. How do you solve non-linear systems of equations?

Tip: Always check your solution by substituting the values back into the original equations to verify they satisfy both equations.